Finite Group DatabasebetaFinite Group DatabasebetaOrder 2400.
864 conjugacy classes of subgroups; only the 191 normal subgroups are shown.
This group has 864 conjugacy classes of subgroups — too many to draw. Only its 191 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C22 | C22×C3⋊(C5⋊D5) |
| commutator, socle, cosocle | C22×C3×C52 | C23 |
| Fitting | C2×C3×C52×D4 | C2 |
| hypercenter | C2×D4 | C3⋊(C5⋊D5) |
| hypocenter | C3×C52 | #127 |
| LCS | G ▷ C22×C3×C52 ▷ C3×C52 | |
| UCS | C1 ◁ C22 ◁ C2×D4 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C2×C3×C52×D4 | C2 | semidirect |
| 2. C2×#10597159 | C2 | semidirect |
| 3. C2×C4⋊(C3⋊(C5⋊D5)) | C2 | semidirect |
| 4. C4×C3⋊#1039 | C2 | semidirect |
| 14. C2×C52×D4 | D3 | semidirect |
| 23. C3×C4×C52 | D4 | semidirect |
| 24. C3⋊#1039 | D4 | semidirect |
| 25. C2×C3×C5×D4 | D5 | semidirect |
| 53. C4×C52 | #67 | semidirect |
| 56. C2×C5×D4 | D15 | semidirect |
| 60. C3×C52 | #127 | semidirect |
| 66. C3×C4×C5 | C22⋊D5 | semidirect |
| 72. C2×C3×D4 | C5⋊D5 | semidirect |
| 88. C52 | #940 | semidirect |
| 101. C4×C5 | #1220 | semidirect |
| 105. C2×D4 | C3⋊(C5⋊D5) | semidirect |
| 107. C3×C5 | #4086 | semidirect |
| 113. C3×C4 | C22⋊(C5⋊D5) | semidirect |
| 130. C5 | #91829 | semidirect |
| 137. C4 | #10597159 | semidirect |
| 138. C3 | #11717260 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C3×C52×D4 | 2 |
| C2×#10597159 | 2 |
| C2×C4⋊(C3⋊(C5⋊D5)) | 2 |
| C4×C3⋊#1039 | 2 |
| #11717260 | 3 |
| #91829 | 5 |